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In the triangle ABC, if AC = radical 2, BC = radical 7, ab = 3, then cosa =?
cosine law
cosA=(AC²+AB²-BC²)／2·AC·AB
=(2+9-7)／2·√2·3
=√2／3
Hope to adopt it with satisfaction
In △ ABC, cosa = radical 3 / 2, ∠ B - ∠ C = 90 ° C = 6, find B A take 60 degrees
In ∵ ABC, ∵ a = 60 B + ∠ C = 120 ? B B C = 90 B = 105 °, C = 15 ° ? C = 6 ? B / sin105 ° = 6 / sin15 ° ? B = 60 ° + 45 °, 15 ° = 45 ° - 30 ° ? B = 6sin (60 ° + 45 °) / sin (45 ° - 30 °) = 6 (sin 60 ° - 30 °) = 6 (sin 60 ° + 45 °) / sin (45 ° - 30 °) = 6
In △ ABC, B = 60 degrees, cosa = 4 / 5, B = radical 3 Find: 1. The value of sinc 2. The area of △ ABC
1. Sina = 3 / 5 ∵ a + B = π - C ∵ sinc = sinc = sin (π - C) = sin (a + b) = sinacosb + cosasainb = 3 / 5 * 1 / 2 + 4 / 5 * 1 / 2 + 4 / 5 * √ 3 / 2 = (3 + 4 √ 3) / 102; according to the theorem of the sine, a / Sina = B / SINB
Known: △ ABC, ab = AC, ∠ a = 120 °, BC = 8, root sign 6, calculate the area of △ ABC
Do ad ⊥ BC in D
∵ AB = AC, ᙽ ABC is an isosceles triangle
﹤ BD = CD = 1 / 2BC = 4 pieces of 6 pieces
∠B=1/2(180°-∠A)=1/2(180-120)=30°
Ad = bdtan30 ° = 4 root number 6 * root number 3 / 3 = 4 root number 2
S △ ABC = 1 / 2bd * ad = 1 / 2 * 8 root number 6 * 4 root number 2 = 16 root number 12 = 32 root number 3
In the triangle ABC, the angle c = 90 degrees, if BC: ab = 1:3, AC = 6 times the root sign 3, find the area of the triangle ABC
If BC is x, then AB is 3x
According to the Pythagorean theorem, (3x) square - xsquare = 6 times the square of root 3
The root 8 of x = 9 times 2 is obtained
S = 9 times 2 times 8 times 6 times 3 times 1 / 2
=27 times root 24
In △ ABC, ∠ C = 90 °, a + B = 2, root number 6, C = 3, root number 2, calculate the area of △ ABC
In the triangle ABC, the angle c = 90 degrees
= (2) B = (2) a ^ 2
Because C = 3 root sign 2, a + B = 2 root number 6
So 18 = 24 -- 2Ab
2ab=6
ab=3
Because in the triangle ABC, the angle c is 90 degrees
So the area of the triangle ABC = (AB) / 2
=3/2.
In the triangle ABC, angle c = 90, ab = 6, BC = 3, root sign 3, find the area of angle a, AC and triangle ABC
Angle a = 60 angle B = 30 AC = 3 s = 9 √ 3 / 2
As shown in the figure, ⊙ o passes through points B and C. the center O of the circle is inside the isosceles right angle △ ABC, ∠ BAC = 90 °, OA = 1, BC = 6, then the radius of ⊙ o is () A. Ten B. 2 Three C. 3 Two D. Thirteen
A is used as ad ⊥ BC. From the meaning of the title, ad must pass through point O and connect to ob;
∵ △ BAC is an isosceles right triangle, ad ⊥ BC,
∴BD=CD=AD=3；
∴OD=AD-OA=2；
In RT △ OBD, according to Pythagorean theorem, it is concluded that:
OB=
BD2+OD2=
13．
Therefore, D
In the right triangle ABC, the angle BAC = 90 degrees BC = 6, if the circle O passes through the point B C OA = 1, find the radius of the circle o
This problem is a plane analytical problem. The point O is on the vertical line of BC, and OA = 1. It is better to take a as the center of the circle and 1 as the radius to make a circle. O is the intersection point of a straight line and a small circle. This problem should be a few conditions, and the idea is the one above~
As shown in the figure, a circle O with radius R is inscribed into an isosceles right triangle ABC, A radius of R, then R is 5 points better than R A circle O of radius R is circumscribed to this triangle, then R is greater than R
R: R = radical 2 + 1
RELATED INFORMATIONS
- 1. Known: as shown in the figure, in the right triangle ABC, the angle c = 90 degrees, the point O is the center of the circle, the length of OA is the radius of the circle, and AC, AB intersect with point D.E, and the angle CBD = angle a.bd is the tangent line of circle O. find: if ad: Ao = 8:5, BC = 2, find the length of BD
- 2. Point O is a point in △ ABC, ∠ ABO = 25 degrees, ∠ ACO = 35 degrees, and the degree of ∠ BOC is 5 degrees less than 2 times of ∠ a In △ ABC, the top angle is ∠ a, the left is ∠ ABC, and the right is ∠ ACB
- 3. In △ ABC, if the bisectors of ∠ a = 50 °, B and C intersect at point O, then the degree of ∠ BOC is () A. 65° B. 100° C. 115° D. 130°
- 4. As shown in the figure, in the RT triangle ABC, the angle B = 90 degrees. If the distance between the point O and the triangle three times is equal, what is the angle AOC? For detailed explanation
- 5. It is known that: as shown in the figure, in △ ABC, the bisector of ∠ B and the bisector of external angle of △ ABC intersect at point D, ∠ a = 90 °
- 6. It is known that the distance between point O and AB and AC is equal, and ob = OC (1) As shown in Figure 1, if point O is on edge BC, it is proved that ab = AC; (2) As shown in Figure 2, if point O is inside △ ABC, it is proved that ab = AC; (3) If point O is outside △ ABC, is ab = AC true? Please draw a picture to show it
- 7. In the triangle ABC, BC = 2, Sina = 2 / 3, root 2, then what is the maximum product of AB vector and AC vector
- 8. In △ ABC, Tanc = 3, radical 7 (1) find COSC (2) if vector CB · vector CA = 5 / 2 and a + B = 9 find C Process
- 9. In the triangle ABC, a = 60 degrees, AC = 16, area s = 220, root number 3, then BC = what?
- 10. An obtuse triangle ABC, ∠ B is an obtuse angle, where AB = 10, BC = 9, AC = 17, find the height on BC side
- 11. As shown in the figure, it is known that ∠ AOB = 30 ° and the point P is inside ∠ AOB, Op = 6. If there is a moving point m on OA and a moving point n on ob, then the minimum perimeter of △ PMN is______ .
- 12. As shown in the figure, the side of the cone is cut along OA, and the fan-shaped OAB is expanded into a plane figure (1) What is the relationship between the length of the sector arc AB and the length of the circle at the bottom of the cone? What is the position relationship between point a and point B on the side of the cone? (2) If the angle ∠ AOB = 90 °, what is the relationship between the radius r of the cone bottom circle and the radius r of fan-shaped OAB (i.e. OA or OB)? (3) If point a moves on the side of the cone and then returns to its original position, how should the shortest distance of point a be designed? If R 2 = 0.5, ∠ AOB = 90 °, find the shortest distance of point a
- 13. The right angle vertex P of the triangle ruler slides on the ray OM, and the two right angle sides intersect OA and ob at point CD respectively Conjecture the quantitative relationship between PC and PD
- 14. As shown in the figure, OA, OB and OC are the radii of circle O. if ∠ AOB = 2 ∠ BOC, please judge whether ∠ ACB = 2 ∠ BAC is tenable. Why?
- 15. As shown in the figure, the ray OA, ob, OC, OD have common endpoint o, and ∠ AOB = 90 °, COD = 90 °, AOD = 5 4 ﹤ AOC. calculate the degree of ﹤ BOC
- 16. In the plane rectangular coordinate system, the image of function y = - 3 / 4x + 6 intersects X axis and Y axis at point a and B respectively, line BC and X axis intersect at C, and point C is the midpoint of line OA Find out whether there is a point m on the straight line AB so that △ BCM is an isosceles triangle. If there is, find out the coordinates of point M
- 17. Known: as shown in the figure, find a point P on the straight line Mn, so that the distance between the point P and the two sides of ∠ AOB is equal (the method is required to be written, the drawing trace shall be retained, and the conclusion shall be written)
- 18. As shown in the figure, ∠ AOB = 30 ° OC bisection ∠ AOB, P is a point on OC, PD ‖ OA intersects ob at point D, PE ⊥ OA at e, OD = 4cm, then PE ⊥ OA is at point E=______ .
- 19. The bottom surface of four pyramids P-ABCD is square, and the bottom surface of PB ⊥ ABCD proves that no matter how the height of four pyramids PB changes, the surface PAD and the surface PCD cannot be vertical
- 20. It is known that: as shown in the figure, P is the interior point of the square ABCD, ∠ pad = ∠ PDA = 15 °. Verification: △ PBC is an equilateral triangle